What is an Arithmetic Series?
An arithmetic series is the sum of the terms of an arithmetic sequence, a sequence of numbers in which the difference between consecutive terms is constant.
Formula for Arithmetic Series
The sum of the first n terms (Sn) of an arithmetic series is given by:
Sn = n/2 × (first term + last term)
Example
Consider the series: 2, 4, 6, 8, 10. The sum of this series can be calculated as:
- Number of terms (n) = 5
- First term = 2
- Last term = 10
- Sum, Sn = 5/2 × (2 + 10) = 30